I agree that both wheels need to turn or do 3 point turns instead. Personally, I've never seen a ZTR that doesn't rut up the lawn. It's just the nature of the beast. It really does take a skilled operator to avoid tearing up the ground.
Sometimes if I decide not to do a 3 point turn, I will pulse the inside wheel with the stick several times until I'm lined up. This tends to lesson the rutting.